Question: Stephanie is 3 times as old as Daniel. Eight years ago, Stephanie was 7 times as old as Daniel. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Stephanie and Daniel. Let Stephanie's current age be $s$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $s = 3d$ Eight years ago, Stephanie was $s - 8$ years old, and Daniel was $d - 8$ years old. The information in the second sentence can be expressed in the following equation: $s - 8 = 7(d - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = s / 3$ . Substituting this into our second equation, we get: $s - 8 = 7($ $(s / 3)$ $- 8)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 8 = \dfrac{7}{3} s - 56$ Solving for $s$ , we get: $\dfrac{4}{3} s = 48$ $s = \dfrac{3}{4} \cdot 48 = 36$.